I'm not aware of any such fanfic. Naruto is a male character in the series, and such a concept goes against the natural order of the Naruto universe. Fanfics usually follow the general theme and characteristics of the original work, and this seems quite out of place.
In some fanfictions, it could be due to a special jutsu gone wrong. Maybe a jutsu that Kakashi was using to transfer some of his chakra to Naruto for a mission accidentally transferred his Sharingan power as well.
If Naruto was raised by Kakashi in fanfiction, their relationship would be very different from the original. Kakashi could teach Naruto more about the Sharingan and its secrets since he has one. Naruto might also inherit some of Kakashi's reading habits and love for Icha - Icha Paradise, which could lead to some really funny moments.
Often, in 'naruto gets trained by kakashi fanfiction', Naruto will face various challenges during the training. These challenges could be physical, like enduring intense sparring sessions with Kakashi. Or they could be mental, such as understanding complex ninja concepts. Through these experiences, Naruto not only becomes more powerful but also gains a deeper understanding of himself and his ninja path. This might also lead to him forging a stronger bond with Kakashi, which could play a significant role in future plot developments.
In some fanfictions, when Kakashi finds Naruto, it could be a situation where Naruto is in danger. Kakashi would then rescue him and from that moment on, their bond becomes even stronger. Kakashi might then focus on helping Naruto control the Nine - Tails' chakra more effectively, which would change the course of Naruto's development in the story.
Another situation is when Kakashi is on a solo mission. He might encounter a group of powerful opponents who manage to wound him. This forces him to rely on his wits and basic ninja skills to survive while waiting for backup. It can show his resourcefulness even when injured.
In this fanfiction, Naruto's character development is multi - faceted. Physically, he becomes stronger and faster through the rigorous training. Mentally, he learns patience. Kakashi's training methods might include waiting for the right moment to strike or endure long periods of stealth. This teaches Naruto to be more patient in combat and in life. Emotionally, he matures. He may face setbacks during the training and learn to deal with failure in a more constructive way. Instead of getting frustrated and giving up, he uses it as a motivation to improve. All these aspects combined shape Naruto into a more well - rounded and capable ninja.
Well, Naruto might gain new abilities. He could potentially use the Sharingan's powers like predicting movements better in combat. It would be a huge boost to his already formidable skills.
The non - existence could be due to multiple factors. In the Naruto world, there are established rules and norms. Males don't get pregnant in that world - view. Moreover, the Naruto series has a strong following and a large community. Such a fanfic would likely be rejected by the majority of the fans because it goes against the essence of the series. The series is about ninjas and their adventures, not about such abnormal and inappropriate relationships. Also, from a creative perspective, it would be extremely challenging to write a story that could make this plot seem even remotely reasonable within the framework of the Naruto universe.
Their relationship could develop very quickly. Kakashi might see Naruto as a prodigy waiting to be shaped. He would start mentoring Naruto intensively, and Naruto would look up to Kakashi like a father figure. They'd probably go on missions together more often, and Naruto would learn a great deal from Kakashi's battle strategies.